$\"\"$

\

The series is $\"\"$ .

\

Consider $\"\"$ .

\

Hence $\"\"$ .

\

Substitute the corresponding values in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

When the series is converges if $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Hence the center of series is $\"\"$ and the radius of convergence is $\"\"$ .

\

$\"\"$

\

The series is $\"\"$ .

\

When $\"\"$ the series $\"\"$ is diverges.

\

When $\"\"$ the series $\"\"$ is diverges.

\

When the series is converges if $\"\"$ .

\

Therefore, the series is converges in the interval $\"\"$ .

\

$\"\"$

\

The series is converges in the interval $\"\"$ .